Ex 2: Distributive property to simplify | Linear equations | Algebra I | Khan Academy

TL;DR

Simplify the given equation by clearing out the fractions and then isolate x to find its value.

Transcript

Solve for x. And we have x minus 8 is equal to x/3 plus 1/6. Now the first thing I want to do here-- and there's multiple ways to do this problem-- but what I want to do is just to simplify the fraction. I'm going to multiply everything times the least common multiple of all of these guys' denominators. This is essentially x/1. This is 8/1, x/3, 1/... Read More

Key Insights

• ✖️ Simplifying fractions by multiplying everything by the least common multiple can help clear out the fractions in an equation.
• 🆘 Isolating variables on one side of the equation helps in solving for the unknown value.
• 🙃 Dividing both sides by a coefficient can remove that coefficient, allowing for the solution to be found.

Questions & Answers

Q: How can we simplify the equation by clearing out the fractions?

To clear out the fractions, multiply everything by the least common multiple of the denominators. This will result in a straightforward equation with integer coefficients.

Q: Why do we isolate the x variables on one side of the equation?

Isolating the x variables allows us to solve for the value of x without any other terms. It simplifies the equation and makes it easier to find the solution.

Q: How do we find the value of x after isolating it?

After isolating x, divide both sides of the equation by the coefficient of x to make it equal to 1. This reveals the value of x, which in this case is 49/4.

Q: Is it necessary to check the solution using the original equation?

Although it's not necessary, it's a good practice to check the solution by substituting x back into the original equation. If the equation holds true, then the solution is correct.

Summary & Key Takeaways

• To solve the equation, simplify the fraction by multiplying everything by the least common multiple of the denominators.

• Isolate the x variables on one side of the equation by subtracting 2x and adding 48 to both sides.

• Divide both sides by 4 to get x, and the solution is x = 49/4.